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PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS.
1. Fundamental Principles of Counting.The Rules of Sum and Product.Permutations.Combinations: The Binomial Theorem.Combinations with [...] Catalan Numbers (Optional).Summary and Historical Review.2. Fundamentals of Logic.
Basic Connectives and Truth Tables.Logical Equivalence: The Laws of Logic.Logical Implication: Rules of [...] Use of Quantifiers.Quantifiers, Definitions, and the Proofs of Theorems.Summary and Historical Review.3. Set Theory.
Sets and [...] Operations and the Laws of Set Theory.Counting and Venn Diagrams.A First Word on [...] Axioms of Probability (Optional).Conditional Probability: Independence (Optional).Discrete Random Variables (Optional).Summary and Historical Review.4. Properties of the Integers: Mathematical Induction.
The Well-Ordering Principle: Mathematical Induction.Recursive [...] Division Algorithm: Prime [...] Greatest Common Divisor: The Euclidean [...] Fundamental Theorem of Arithmetic.Summary and Historical Review.5. Relations and Functions.
Cartesian Products and Relations.Functions: Plain and [...] Functions: Stirling Numbers of the Second Kind.Special [...] Pigeonhole Principle.Function Composition and Inverse Functions.Computational Complexity.Analysis of Algorithms.Summary and Historical Review.6. Languages: Finite State Machines.
Language: The Set Theory of Strings.Finite State Machines: A First Encounter.Finite State Machines: A Second Encounter.Summary and Historical Review.7. Relations: The Second Time Around.
Relations Revisited: Properties of Relations.Computer Recognition: Zero-One Matrices and Directed Graphs.Partial Orders: Hasse Diagrams.Equivalence Relations and Partitions.Finite State Machines: The Minimization Process.Summary and Historical Review.
PART 2. FURTHER TOPICS IN ENUMERATION.
8. The Principle of Inclusion and Exclusion.The Principle of Inclusion and Exclusion.Generalizations of the Principle.Derangements: Nothing Is in Its Right [...] Polynomials.Arrangements with Forbidden Positions.Summary and Historical Review.9. Generating Functions.
Introductory Examples.Definition and Examples: Calculational Techniques.Partitions of [...] Exponential Generating [...] Summation Operator.Summary and Historical Review.10. Recurrence Relations.
PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS.
1. Fundamental Principles of Counting.The Rules of Sum and Product.Permutations.Combinations: The Binomial Theorem.Combinations with [...] Catalan Numbers (Optional).Summary and Historical Review.2. Fundamentals of Logic.
Basic Connectives and Truth Tables.Logical Equivalence: The Laws of Logic.Logical Implication: Rules of [...] Use of Quantifiers.Quantifiers, Definitions, and the Proofs of Theorems.Summary and Historical Review.3. Set Theory.
Sets and [...] Operations and the Laws of Set Theory.Counting and Venn Diagrams.A First Word on [...] Axioms of Probability (Optional).Conditional Probability: Independence (Optional).Discrete Random Variables (Optional).Summary and Historical Review.4. Properties of the Integers: Mathematical Induction.
The Well-Ordering Principle: Mathematical Induction.Recursive [...] Division Algorithm: Prime [...] Greatest Common Divisor: The Euclidean [...] Fundamental Theorem of Arithmetic.Summary and Historical Review.5. Relations and Functions.
Cartesian Products and Relations.Functions: Plain and [...] Functions: Stirling Numbers of the Second Kind.Special [...] Pigeonhole Principle.Function Composition and Inverse Functions.Computational Complexity.Analysis of Algorithms.Summary and Historical Review.6. Languages: Finite State Machines.
Language: The Set Theory of Strings.Finite State Machines: A First Encounter.Finite State Machines: A Second Encounter.Summary and Historical Review.7. Relations: The Second Time Around.
Relations Revisited: Properties of Relations.Computer Recognition: Zero-One Matrices and Directed Graphs.Partial Orders: Hasse Diagrams.Equivalence Relations and Partitions.Finite State Machines: The Minimization Process.Summary and Historical Review.
PART 2. FURTHER TOPICS IN ENUMERATION.
8. The Principle of Inclusion and Exclusion.The Principle of Inclusion and Exclusion.Generalizations of the Principle.Derangements: Nothing Is in Its Right [...] Polynomials.Arrangements with Forbidden Positions.Summary and Historical Review.9. Generating Functions.
Introductory Examples.Definition and Examples: Calculational Techniques.Partitions of [...] Exponential Generating [...] Summation Operator.Summary and Historical Review.10. Recurrence Relations.
Details
Erscheinungsjahr: | 2013 |
---|---|
Medium: | Taschenbuch |
Inhalt: | Kartoniert / Broschiert |
ISBN-13: | 9781292022796 |
ISBN-10: | 1292022795 |
Sprache: | Englisch |
Einband: | Kartoniert / Broschiert |
Autor: | Grimaldi, Ralph |
Auflage: | 5 ed |
Hersteller: | Pearson Education Limited |
Verantwortliche Person für die EU: | preigu, Ansas Meyer, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de |
Abbildungen: | Illustrations |
Maße: | 269 x 220 x 52 mm |
Von/Mit: | Ralph Grimaldi |
Erscheinungsdatum: | 14.08.2013 |
Gewicht: | 2,256 kg |
Details
Erscheinungsjahr: | 2013 |
---|---|
Medium: | Taschenbuch |
Inhalt: | Kartoniert / Broschiert |
ISBN-13: | 9781292022796 |
ISBN-10: | 1292022795 |
Sprache: | Englisch |
Einband: | Kartoniert / Broschiert |
Autor: | Grimaldi, Ralph |
Auflage: | 5 ed |
Hersteller: | Pearson Education Limited |
Verantwortliche Person für die EU: | preigu, Ansas Meyer, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de |
Abbildungen: | Illustrations |
Maße: | 269 x 220 x 52 mm |
Von/Mit: | Ralph Grimaldi |
Erscheinungsdatum: | 14.08.2013 |
Gewicht: | 2,256 kg |
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